遙測是指在衛星上或飛機上測量地表資訊而不需要接觸到目標。近年遙測科技蓬勃發展，而高光譜影像為遙測影像中重要的產品，它能同時利用許多感應器用來紀錄不同波段的電磁波能量值，它的光譜數量可以到達數百或數千個波段，因為高光譜有著很高的光譜解析率，所以可以分辨目標物的細微不同。 然而在空間解析度，一個像素中往往會包含多於一種物質，所以需要將物質萃取出來並估計物質的含量，這稱為像素分解。線性混合模型是目前最廣泛應用的，它假設光線沒有多次反射，也就是光經過物質反射後直接到達感測器，因此我們可以利用線性分解計算每種物質在此像素中的含量。不過若地表粗糙或因為地形複雜等原因，線性混合模型有所不足，所以有科學家提出了廣義雙線性模型，此模型加入的光在不同物質間的交互作用，然而此模型忽略了相同物質的交互作用，因此在此研究中。我們提出了一個新的模型叫做修正後的廣義雙線性模型，此模型建立在廣義雙線性模型上，加入了同物質間的交互作用，而此模型也包含了一些物理上的限制，其中包含了物質含量非負數和總合為1，同時限制了二次反射的參數式介於0到1之間。我們利用三組不同的高光譜影像來做測試，修正後的廣義雙線性模型除了可以得到此地區更多的資訊外，計算結果也好於另外兩種模式。 ;Remote sensing is to measure the object properties on the earth’s surface using data acquire from aircrafts and satellites. Hyperspectral imaging spectrometers record electromagnetic energy scattered in their instantaneous field of view with hundreds or thousands of spectral channels. This high spectral resolution improves the capability for material identification via spectroscopic analysis. However, because of spatial resolution, each pixel in hyperspectral images usually contains more than one material. Linear mixture model (LMM) is developed for this problem and has been widely studied. This model assumes that the spectrum of a pixel is linearly combined by all the resident materials with their corresponding abundance, and it ignores the reflection between materials. Nonlinear models have recently drawn lots of attentions for spectral unmixing. The generalized bilinear model (GBM) has been proposed for nonlinear mixture which considers the second order interactions between two different endmembers. However, it neglects the possibility of second order interactions between the same endmembers. In this study, we propose a modified GBM (MGBM) by considering second order reflection between all the endmembers. The non-negativity and sum-to-one constraints for the abundances are ensured by the proposed algorithms.
